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This work focuses on the design improvement of the long-short blades (LSB) impeller by using pitched short blades (SBs) to regulate the flow field in the stirred vessel. After mesh size evaluation and velocity field validation by the particle image velocimetry, large eddy simulation method coupled with sliding mesh approach was used to study the effect of the pitched SBs on the flow characteristics. We changed the inclined angles of the SBs from 30° to 60° and compared the flow characteristics when the impeller was operated in the down-pumping and up-pumping modes. In the case of down-pumping mode, the power number is relatively smaller and vortexes below the SBs are suppressed, leading to turbulence intensification in the bottom of the vessel. Whereas in the case of up-pumping mode, the axial flow rate in the center increased significantly with bigger power number, resulting in more efficient mass exchange between the axial and radial flows in the whole vessel. The LSB with 45° inclined angle of the SBs in the up-pumping mode has the most uniform distributions of flow field and turbulent kinetic energy compared with other impeller configurations.

Circular feed spacers are used to enhance flow mixing in membrane modules and thereby improve their efficiency. However, this involves increased fouling when the spacers are mounted in a zigzag arrangement or high power consumption when submerged. In view of this, a two-dimensional computational model of fluid flow and mass transfer is used to investigate the impact of using an undulated insert as a turbulence promoter in a membrane application. Thus, this study focuses on the effect of varying the amplitude and wavelength of the insert on desalination performances of a narrow channel bounded by two semi-permeable membranes. According to computational fluid dynamics (CFD) simulations, under the considered operating conditions, the increase of the insert amplitude from 0.2 to 0.7 mm could reduce the salt accumulation on the membrane walls by ~ 2.7%, improve the permeate flux by ~ 1%, but drastically increase the axial pressure drop by ~ 1148%. Increasing the insert wavelength from 3 to 24 mm could promote salt accumulation on the membrane walls by ~ 4.8%, reduce the permeate flux by ~ 1.4%, but minimize the axial pressure drop by ~ 96%. Plots of the Sherwood number versus the Power number highlighted that the optimal insert must have a low amplitude and a short wavelength. Some of the insert geometries tested in this study generated better performances than commercial feed spacers, confirming the benefits of undulated inserts and suggesting their use in membrane separation processes.

A comprehensive CFD study was conducted to understand the hydrodynamics characteristics in a top-covered unbaffled stirred tank. The turbulent flow in the tank was described by the Reynolds stress turbulence (RST) model, and the impeller rotation was simulated using a single reference frame (SRF) approach. The flow field and power number in the tank stirred by a Rushton turbine were investigated firstly. It is found that circumferential flow is dominant in the unabffled tank, and the flow field can be divided into forced and free vortex zones. A weak two-loop flow pattern forms in the vertical plane, and would evolve into one single-loop when impeller was equipped very close to the bottom of the tank. In general, impeller off-bottom clearance and blade thickness have small effects on flow field in the unbaffled tank. With increasing of rotational speed, the dimensionless liquid velocity rises, especially near the critical radius of two zones. Critical radius is larger for larger impeller, while the variation range of critical radius to impeller diameter ratio is narrow. The effects of operational and geometric parameters on impeller power number (Np) in unbafffled tank are far different from those in baffled tank. In the unbaffled stirred tank, rotational speed, blade thickness and impeller off-bottom clearance have small effects on power number, while impeller diameter has a significant effect on power number. Under the same operating condition, the larger the impeller diameter, the smaller the power number is. Finally, the hydrodynamics characteristics in the tank stirred by four common impellers were investigated and compared.

Numerical simulations were conducted to investigate transient power consumption characteristics in an unbaffled stirred tank. The transient flow field in the stirred tank was simulated using a shear-stress transport k–ω turbulent model. Meanwhile, the transient power number was analyzed based on the predicted impeller torque. The accuracy and reliability of the simulations were verified by experimental data in the literature. The simulation results show that power number undergoes four stages, i.e., plateau value, sharp falling, slow falling and stable stages, after impeller is suddenly started up in quiescent fluid. The curve of transient power number versus dimensionless time is hardly affected by the impeller start-up speed. When impeller speed is accelerated from the same initial speed to higher end speed, the plateau power number becomes higher and the time interval is shorter. With the same speed increment, the plateau power number falls for higher initial speed. Power number falls sharply and then rises gradually to a steady value after impeller speed is decelerated from high to low speed. Time is longer for the power number reaching to steady state when impeller speed is decelerated from same initial speed to lower end speed.

The performance of curved bladed turbines (CBTs) for the agitation of Newtonian fluids in cylindrical tanks is investigated. The efficiency of CBT is compared with that of the standard Rushton turbine. Also, effects of the blade height of the new designed impeller are highlighted. The computational fluid dynamics (CFD) study is performed to observe the axial, radial and tangential components of velocities, flow patterns and power consumption. The obtained results revealed that the increase of blade curvature reduces the power consumption. Also, a slight decrease of power number is observed in the turbulent flow regime within unbaffled tanks. In a comparison between the cases studied, the best axial circulation of fluid is given by the impeller with flat blades. The increase of the height of curved blades has generated a stronger tangential flow and enhanced the axial movement of fluid particles, but with further penalty in power input.

The volumetric mass transfer coefficient (kLa) is one of the most important parameters for design and scale-up of gas–liquid–solid three-phase mechanically stirred tank reactors. In this work, the effects of agitation speed, superficial gas velocity, temperature, and volumetric solid concentration (CV) on the power consumption and kLa were discussed and quantitatively analyzed. In an air-water-glass beads system, the gassed power number (NPG) and kLa increase remarkably with the temperature. At ambient temperature, kLa decreases significantly with increasing CV with a power law exponent of 3.10, but this decreasing effect becomes weaker at higher temperatures. In this hot-sparged three-phase system, the addition of solids slows down the increasing tendency of NPG with the temperature, but enhances the increasing tendency of kLa. The increase in temperature weakens the decreasing effect of CV on kLa. Compared with the effect of temperature on NPG and kLa, the effect of CV is nearly negligible. As a practical guide to industrial applications, it is more effective to enhance the gas–liquid mass transfer by increasing the temperature or power consumption than by changing CV or increasing superficial gas velocity. The empirical correlations of power consumption and kLa obtained in this work can provide helpful guidance for the industrial design and operation of hot-sparged three-phase stirred tank reactors.

The impeller geometry is a determining factor for mixing efficiency in a stirred vessel. In this study, the effect of disc-blade intercepting angle on power number, just suspended speed and mass transfer coefficient was investigated in a multiphase system under turbulent conditions. The impellers used in this study were fabricated with 3D printing. The interactions between the experimental parameters were analysed using Response Surface Methodology (RSM). The impeller power number was found to have a linear positive relation with disc-blade intercepting angle from 30° to 90°. Beyond 90°, the impeller power number became lower with increment in the disc-blade intercepting angle. The results confirmed better suspension efficiency in the angle range of 50° to 120° in 5 wt% solid suspensions. The lowest specific power requirement (Ɛjs) at just suspension condition was observed in the angle range of 30° to 80°. The highest mass transfer coefficient was obtained for the impellers with disc-blade intercepting angle in the middle range. Two models were established on power number and mass transfer coefficient for various disc-blade intercepting angles. The study confirmed that the hydrodynamic and mass transfer performance of disc blade impellers could be maximized by changing the disc-blade intercepting angle for a selected system.

With the increasing demands for the high efficiency of pulp-mixing, which is adapted to the fine particles entering into flotation section, an intensification pulp-mixing device with novel design has been developed. On the basis of numerical simulation, which indicated efficient circulation and shear effect of the “maleic-cutting” configuration equipped with static-guide-blade, the power dissipation amount PV, mixing time θm, power number NP, mixing time number Nθ, CS which reflects shear property, suspension percentage φ/Φ(%), and concentration variance σ2 were measured, analyzed and compared with the ordinary agitated tank. Combining with actual mineral separation tests, performance of the efficient pulp-mixing device characterized by “multi-stage and compulsory” has been validated: the “multi-stage and compulsory” mixing device corresponds to a different circulation/shear energy; under the same operating conditions, the absolute advantages in the aspect of mixing time are the root cause for the increase of mixing efficiency; the “maleic-cutting” configuration is less influenced by pulp-mixing time and has the characteristics of achieving fast mixing; the strong shear effect mechanism is the root cause for the realization of pulp-mixing intensification on fine-particle and microfine-particle materials. Therefore, the “multi-stage and compulsory” mixing device designed by this research successfully accomplished intensification of pulp-mixing effect.

In this study, the effect of height/diameter (H/D) ratio and type of impeller on the power consumption of the agitator in the Continuous Stirred Tank Reactor (CSTR) was analyzed. CSTR in the process of producing nitrocellulose from cotton linters with a production capacity of 10,000 tons/year was used as a case study. In designing a CSTR, power consumption is also considered because it is related to techno-economics. The results show that it is necessary to adjust the amount of impeller related to the H/D ratio value because it can affect the level of liquid in the reactor during the stirring process so that it also affects the reaction conversion. This work shows that with the higher H/D ratio, the greater number of impellers needed and increase the agitator power consumption. For specific applications, the number of impellers (NT) must be increased to meet the minimum power consumption. As the result, this work recommends the optimal H/D ratio for CSTR design is the maximum H/D ratio to get the NT-calculation as close as to the NT-taken while satisfying the minimum power consumption required. The optimal H/D ratio can be different depending on the impeller type and application.

Citric acid transport facilitation in electrodialysis was investigated using different flow promoter geometries e.g. rod, twisted tape (TT), rectangular winglet (RW) shape vortex generator (VG) and helical screws at four different flow rates 5, 10, 15 and 20 LPH. Flow visualization of 39 promoters (shape, spacing and orientation) were performed using 3D simulation (COMSOL Multiphysics® 5.3a). Based on simulation results, 14 best promoters were selected for experimental determination of ion transport and power consumption from Sherwood number, Sh and Power number, Pn respectively. With increase in flow rate and reduced spacing, Sh increased along with Pn. Mesh type TT performed better than mono layer TT but pressure drop increased. Screw promoter placed parallel to flow showed higher Sh and Pn compared to rod, VG and TT. 50% rise in Sh was noted with helical screw (d/h = 1.33, α = 90°) relative to empty channel. 1.5 times rise in LCDs were noted with conducting TT compared to non-conducting TTs with barely 1.5% increase in Pn. LCDs with conducting TTs were 80% higher compared to empty channel.

Power characteristic of a rotationally reciprocating impeller was investigated in view of torque variation using Newtonian and viscoelastic fluids. The power curve for both fluids showed good agreement by the introduction of the appropriate definition of Reynolds number based on Metzner–Otto concept. The raw date of torque variation was decomposed into sinusoidal waves having various frequencies (higher harmonics) with the help of FFT. The phase difference of the first harmonic against reciprocating motion showed that the torque variation was significantly affected by elasticity at low Reynolds numbers, where the dimensionless intensity was inversely decreased against Reynolds number similar with power number. It is found for viscoelastic fluid that the relative intensity and phase difference of the third harmonic were roughly constant except for viscous dominant region. Since those information of higher harmonics are cancelled in the calculation of time-averaged power consumption, it is found that the frequency analysis of torque variation is useful to elucidate dominant factors on torque variation and probably on fluid flow generated by a rotationally reciprocating impeller.

Different approaches have been reported in the literature that aim to improve the performance of reverse osmosis (RO) desalination plant operations, attempting to make the desalination process more efficient. This study investigates the performance of four commercial feed spacers for spiral wound reverse osmosis modules by considering energy consumption and production capacity, as well as their combination, through a previously proven approach to computational fluid dynamics (CFD) modelling. Among the performance measures studied, SCE (spacer configuration efficacy), SPC (specific power consumption) and Pn (power number) showed a high level of predictability (R2 ≥ 0.998, 0.994 and 0.994, respectively) through power law correlations of Re with two spacer-dependent parameters. Of the four commercial spacers investigated, the DelStar Technologies Naltex N05013_90HDPE-NAT (“90 HDPE”) spacer has been ranked as the best or second best based on multiple performance measures over the flow range Re = 50–100. Furthermore, the very weak response to flowrate changes observed for 90 HDPE, based on pressure loss, SPC, Pn, Sh and SCE measures, indicates the prospects for energy savings. SPMP′, a modified definition of SPMP (Spacer Performance Ratio), shows no consistent response to flow variations for the spacers studied.

The choice of impeller design in stirred-tank reactors (STRs) affects important process characteristics such as the suspension of particulates, mixing of nutrients or gasses, and the distribution of turbulent kinetic energy and its dissipation rate. A novel impeller, the Bach impeller, has been characterized in this work and its novel geometry and mechanism of action are discussed in detail. Experimental measurements of the power consumption, mixing time, and microparticles suspension dynamics were carried out at the 1 L scale in an unbaffled reactor and the performance compared with two conventional up-pumping axial flow impellers, namely the 3-Blade segment (3BS, also called “elephant ear”) and marine impeller. In addition, the impeller flow number and pumping efficiency were obtained from Particle Image Velocimetry experiments. The Bach impeller exhibited a low power number of NP=0.36 and showed it can generate a uniform suspension of microcarriers even at relatively low impeller speeds (from N=25-30 rpm onwards). The impeller was found to effectively mix the reactor volume within tM=25 s at N>50 rpm (i.e. NtM=37±5) at a higher clearance when it was mounted closer to the free surface, C/T>0.5, while minimally affecting its suspension capabilities. Lastly, the Bach impeller displaced more fluid than the marine impeller and roughly an equal amount to the 3BS impeller, suggesting that the novel impeller can successfully be used for STR processes in the (bio)chemical engineering industry where low power inputs, but high mixing and particle suspension efficiencies are sought.

A side-entry propeller was designed and introduced in this study. The mixing performance of shear thinning fluids in a cylindrical stirred vessel equipped with this propeller was experimentally investigated via an ultrasonic Doppler anemometer (UDA, experimental results were consistent with theoretical findings. The power number and Reynolds number of this propeller were evaluated by using Chhabra, Metzner and Reed equations. Results showed that the power number versus the Reynolds number curves were highly comparable with Metzner and Reed equations. The velocity jet vectors flow field of 320, 380, and 440 rpm were described in detail. These findings demonstrated that the circulation loops, cavern size, and shape were highly influenced by shear thinning parameters and operating conditions. The average of the velocity profiles from five sample lines in front of the propeller was utilized to analyze the effect of rheological properties and operating conditions on the propeller. The axial, radial and tangential 2D velocity profiles located at one sample line (200 mm) in front of the propeller at the design rotation speed were evaluated.

Flow and power characteristics of a two-stage inline axial flow rotor-stator mixer have been investigated via CFD simulation of the RANS equations. The realizable k–e turbulence model with enhanced wall treatment was used to predict the mean velocity field, turbulent kinetic energy, and energy dissipation rate, as well as flow and power number. The results from different computational meshes are compared. The periodic behavior of throughput and torque is attributed to rotor position and shown to be related to number of blades and stator slots. The flow, power number, and energy dissipated in different fluid regions are reported for various backpressure operating conditions.

The results of the power consumption for an agitated vessel equipped with vertical tubular baffles and high-speed impeller are presented in the paper. Aqueous solutions of CMC were agitated within transitional range of the non-Newtonian liquid flow in the agitated vessel of inner diameter equal to 0.6 m. Eight different types of the impellers were tested: Rushton or Smith turbines, turbine with straight blades, pitched blade turbines and propeller. The J tubular baffles of outer diameter B were located in the position e from the vessel wall. Different configurations of baffles, arranged around the vessel circumference singularly or blocked in the modules, were considered in the study. In total, 180 different tubular baffles–impeller systems were tested. The measurements of the torque were conducted by means of the strain gauges method. Based on the power characteristics obtained for each impeller type, the effect of the geometrical parameters of the vertical tubular baffles on the power number was determined and discussed. The results show that geometry of the tubular baffles mostly affects the power number for the system with radial flow Rushton turbine. Moreover, power numbers decrease with the increase of the clearance between baffle and vessel wall for the systems, in which the radially axial circulation of the liquid is promoted. The dependences of the power number on the geometrical parameters of the vertical tubular baffles arranged singularly around the vessel circumference were described by means of the Eqs. (5)–(16). These equations can be useful in the project computations.

In turbulence modeling, the RNG and Realizable models have important improvements in the turbulent production and dissipation terms in comparison to the Standard. The selection of the appropriate turbulence model has an impact on the convergence and solution in STRs, and they are used in mixing, multiphase modeling or as starting solution of transient models as DES and LES. Although there are several studies with the pitched blade turbine (PBT) impeller, most of them used the Standard model as representative of all k–e models, using structured hexahedral grids composed of low number of cells, and in some cases under axial symmetry assumptions. Accordingly, in this work the assessment of the Standard, RNG and Realizable models to describe the turbulent flow field of this impeller, using the Multiple Reference Frame (MRF) and Sliding Mesh (SM) approaches with tetrahedral domains in dense grids, is presented . This kind of cell elements is especially suitable to reproduce complex geometries. Flow velocities and turbulent parameters were verified experimentally by PIV and torque measurements. The three models were capable of predicting fairly the pumping number, the power number based on torque, and velocities. Although the RNG improved the predictions of the turbulent kinetic energy and dissipation rate, the Realizable model presented better performance for both approaches. All models failed in the prediction of the total dissipation rate, and a dependence of its value on the number of cells for the MRF was found.

Radial flow impeller is the energy-intensive and fundamental component in reactors for the gas–liquid transfer process. A newly designed fan-shaped turbine (FT) assembly with annular-sector-shaped concave blades was characterized and compared with the Rushton turbine (RT) and Bakker turbine (BT). A new surface equation was established to design the blade of the FT impeller. Under turbulence conditions, the FT impeller showed a lower power number and higher relative power demand (RPD) compared with RT and BT impellers. The power number of the FT impeller was 1.7, lower by 26% than that of BT impeller. The RPD of the FT impeller was nearly 0.95 at a high impeller speed. The critical dispersion speed, gas holdup, and volumetric oxygen transfer coefficient of the FT impeller were close to those of BT impeller. Moreover, the oxygen transfer efficiency of the FT impeller was remarkably higher by 35%–66% and 23%–34% than that of RT and BT impellers, respectively. The FT impeller showed competence in a broad operation range, strong robustness, energy-saving feature, and efficient mass transfer characteristics.

This study focuses on the macroscopic characteristics of the turbulent flow in a vessel equipped with a newly developed long-short blades (LSB) agitator. After validation by PIV experiments, the LES method using dynamic kinetic energy sub-grid scale model, coupled with sliding mesh approach, was used to investigate the flow patterns, the axial and radial flow rates, turbulent dynamic energy distribution, and the power number in the vessel with the LSB agitator at the liquid height, H / T = 1.0 and 1.5, respectively. It is found that the turbulent characteristics are substantially different from those of the conventional agitators. The short blades of the LSB agitator generate a strong axial up-flow in the center, which interacts with the dominant radial motion of the long blades, leading to formation of multiple vortexes along the axis. The direction of the flow in the vortex above the short blades is opposite to that below the short blades, which is completely different from the classical Rushton turbine. Effective mass exchange between the axial and radial flows occurs nearly in the entire vessel. Compared with the conventional agitators, the LSB agitator can achieve high mixing performance and much better homogeneity in the distribution of the turbulent kinetic energy. The effect of the liquid height on the power number and the specific power consumption was also discussed.

The best-known paper on non-Newtonian fluids in mixing systems is the Metzner and Otto’s work. A central idea of their contribution is based on the assumption that in laminar flow there exists an average shear rate ( γ av ) around the impeller (whose exact location and geometric shape is not clearly specified), and that it is proportional to the impeller speed (N), i.e., γ av = K s N , where Ks is the Metzner-Otto constant. In this work, an in-depth investigation of this assumption is carried out by using computational fluid dynamics (CFD) to calculate the three-dimensional flow induced by a Rushton turbine (RT). It was found that the volume swept by the blades is the region where Ks may be computed explicitly as K s = γ av / N directly from non-Newtonian flow simulations. The obtained Ks values in this region were found in good agreement with reported data. Furthermore, power number measurements and data from literature were used to validate the simulations. The CFD method developed in this study can be used to readily and reliably evaluate Ks of industrial mixing impellers without resorting to power data of Newtonian fluids.

Power characteristics for an agitated vessel equipped with planar short baffles of length L and pitched blade turbine of pitch β are presented in the paper. The studies were carried out in the vessel of inner diameter D = 0.6 m, where the baffles were located in the distance p from the vessel bottom (p + L = H). Torque was measured using strain gauge method within the turbulent regime of the flow of Newtonian liquid in the agitated vessel. The effects of the pitch β and geometrical parameter p/H on the power number Ne were determined mathematically. The results showed that, for the assumed value of the angle β, the function Ne = f (L/H) decreases with the decrease in the baffle length L (i.e. with the increase in the parameter p). Moreover, for the assumed value of the baffle length L, the function Ne = f (β) increases with the increase in the angle β of the inclination of the impeller blade.

In the industrial fermentation processes, most liquids are non-coalescent and often exhibit increased viscosity. However, due to the limitations of most measurement methods, there is a lack of reliable data for predicting volumetric mass transfer coefficients (kLa) for viscous batches, especially under high dissipated energies, as the accurate determination of oxygen concentration profile in viscous liquids is not as easy as in low viscosity ones. Our goal is to develop reliable technique for kLa determination in viscous liquids and to establish suitable correlation shapes to describe kLa data. We used the dynamic pressure method (DPM), the experimental set-up of which has been modified for the measurement in viscous liquids. Dissolved oxygen (DO) probes were placed in bypass measuring cells. This set up brings well defined transient characteristics of DO probes, which is crucial for correct kLa evaluation. Measurements were conducted in two phase multiple-impeller fermenters with a non-coalescent viscous Newtonian batch under a wide range of experimental conditions and in the apparatuses of two scales. Using pure oxygen as gas phase, it was confirmed that DPM yields kLa’s independent of the driving force of absorption even in viscous batch. The improved set up of DPM enabled to use also optical DO probes as well as polarographic ones. It was confirmed that optical DO probe can be used for kLa values up to 0.4 s−1. Based on the experimental data, correlations were developed to predict kLa in industrial fermenters. Standard correlation kLa = 2.99 ⋅ 10−3⋅(Pg/VL)0.891vs0.556 with standard deviation, SD, 30%, based on gassed power input Pg and superficial gas velocity vs, has low standard deviation but it is scale specific. On the other hand, when the term of impeller tip speed (ND) is used instead of Pg, predicted data exhibit neither over- nor under-estimation of kLa for particular apparatus scale; so the effect of the vessel scale is properly described using this term. In addition, the impeller power number Po was found to be a reliable predictor of kLa in a common correlation for various impeller types, when used together with the impeller tip speed term. The correlation kLa = 0.295⋅(ND)2.083vs0.461 Po0.737 with SD 28% suggested in this work can be used for fairly accurate design of industrial fermenters. Both the experimental technique and the correlation shape are ready to be used to obtain the design tool for other batches with various viscosities.

In the present study hydrodynamics and mixing characteristics in a novel batch rotor-stator mixer (RSM), which is very simple in construction and design, is investigated at different rotor speeds (2000, 4000 and 6000 rpm). The proposed RSM design is comprised of tilted jets/holes in the stator, for the deep penetration in the mixing vessel. For the optimization of operating as well as geometrical parameters of the proposed mixer design, simulations are carried out using transient sliding mesh with k-e turbulence model at different rotor speeds. It was observed that besides radial and tangential flows jets emerging from stator holes impinge the bulk fluid above and below the stator, which improves mixing and reduces dead zones. Further, the flow parameters such as mass flow rate, Power number, Flow number, pumping efficiency and energy dissipation rate increased with an increase in rotor speed. Further, the energy dissipation rate is found maximum in the rotor swept region. It is observed that the amplitude fluctuations in flowrate and torque, with blade position, increased with the rotor speed. Further, mixing characterization in the novel RSM is studied for the first time in a batch RSM to predict the dead zones in the RSM.

Computational fluid dynamics (CFD) simulations were applied for evaluating the hydrodynamics characteristics in an uncovered unbaffled tank agitated by pitched blade turbines. A volume of fluid (VOF) method along with a Reynolds stress model (RSM) was used to capture the gas-liquid interface and the turbulence flow in the tank. The reliability and accuracy of the simulations are verified. The simulation results show that the vortex can be divided into central zone and peripheral zone, and flow field in the tank can be divided into forced vortex flow region and free vortex flow region. With the increase of impeller speed, the vortex becomes deeper, while the critical radius of the two zones keeps almost unchanged. The impeller clearance and the rotational direction have little effect on the vortex shape. The vortex becomes deeper with increasing of the impeller diameter or the blade angles at the same rotational speed. Power number is little influenced by the impeller speed, and decreases by about 30% when impeller diameter varies from 0.25T to 0.5T. When blade angle varies from 30° to 90°, power number increases by about 2.32-times. Power number in uncovered unbaffled tank is much smaller than that in baffled tank, but is very close to that in a covered unbaffled tank. The discrepancy of power number in uncovered unbaffled tank and that in covered unbaffled tank is less than 10%.

Glass-lined tanks/reactors provided with a torispherical (dish) bottom and equipped with a retreat-blade impeller (RBI) are commonly used in the industrial syntheses of Active Pharmaceutical Ingredients (APIs). The power, P, dissipated by the RBI in the liquid in the tank is critical to many mixing processes, especially since the power per unit liquid volume, P/V, controls many mixing phenomena. Despite their common industrial use, limited information on P for RBIs and the corresponding nondimensional Power number, Po, is available. Here, P values for an RBI in liquids of very different viscosities at different agitation speeds and for different baffling configurations, i.e., unbaffled, partially baffled (with a single “beavertail” baffle), and fully baffled (four rectangular baffles), were measured experimentally in a scaled-down version of a typical reactor for API synthesis. The corresponding Po values were obtained for a large range of the Reynolds number, Re (1 < Re < 400,000). Po was found to vary s...

International audience; A prototypal convective mixer, designed and built for this work, allows investigating powder rheology under various geometrical configurations. The configuration chosen here is a horizontal vessel with four rectangular blades. Two blade inclinations (0–33°) and three filling ratios are studied for two powders of different kind: a free-flowing powder (semolina) and a cohesive powder (lactose). For the smaller agitation speeds, the flow regime of the powder is rolling and is characterized by surface powder avalanches. For greater agitation speeds, the flow regime is cataracting, with particle projections that follow the blade movement. These flow regimes are identified for both powders and do not depends on the filling ratio. Rheological measurements evidence that the blade inclination has little impact on the mechanical power needed to stir the free-flowing powder. It has an impact observable on cohesive powders, especially for high filling ratios. A correlation between the power number and the Froude number is established and compared to previous results obtained on a different technology. It is of the form: Np = a.Frb. The dependencies of the coefficients a and b on the powder type and on the flow regime are quantified.

Numerical simulations were carried out to investigate the turbulent flow with free-surface vortex in an uncovered unbaffled stirred tank. An Eulerian–Eulerian multiphase flow model coupled with a volume-of fluid method was applied to capture the gas–liquid interface and describe the flow field in the tank. Turbulence is computed using a Reynolds stress model with seven equations. The reliability and accuracy of the simulations are verified by comparing the predicted free surface profiles and power numbers with experimental data in the literature. The overall agreements between the simulation results and experimental measurements are obtained. The simulation results show that vortex on the liquid free surface in the uncovered unbaffled tank can be divided into central zone and peripheral zone, and the critical radius of the two zones keeps almost unchanged with enhancing of impeller speeds. At the same impeller speed, vortex becomes deeper and larger with increasing of impeller diameter. However, vortex shape changes not very much with increasing of impeller diameter under the same power consumption. Impeller clearance has no significant influence on the vortex shape. Circumferential flow is dominant in the uncovered unbaffled tank, and the flow field can be divided into forced vortex region and free vortex region. Power numbers in uncovered unbaffled stirred tanks decrease slightly with increasing of the Reynolds number, and are far lower than that in baffled stirred tanks.

International audience; Mixing of a viscoplastic fluid using Scaba 6SRGT impellers in a cylindrical vessel has been studied. Cuts have been introduced in each blade of the impeller in order to reduce the power requirements. Effects of the cut-height (h2/D = 0, 0.015, 0.04, 0.065 and 0.09, respectively), cut-length (l/D = 0, 0.06, 0.12 and 0.18, respectively), and of the number of cuts (nb = 1, 2, 3, 4, and 5) on the hydrodynamics and power consumption were explored. The suggested designs, compared to the classical Scaba 6SRGT impeller, display a reduction in power number by about 20%, 19.9% and 66.6% when the cut-height, cut-length and number of cuts are changed from h2/D = 0 to 0.09, l/D = 0 to 0.18 and nb = 1–5, respectively. However, the increased surface area of cuts is accompanied by a reduction in the size of radial jet of fluid, resulting thus in a weakened axial flow and a decrease in cavern size. As a result, the best trade-off between the reduced power consumption and enlarged cavern size correspond to the case nb = 3, l/D = 0.12. The reduction in power number for this case is estimated to be as about 15%.

Bio-oxidation leaching of refractory gold concentrate was carried out in a typical gas-liquid-solid three-phase stirred bioreactor. The bacteria, which adhered to solid particle surfaces and spread over the liquid phase, require sufficient oxygen and nutrient of carbon and nitrogen, and then the mass transfer rate should be considered. However, the mass transfer coefficient, which could be used to evaluate the mass transfer rate, was determined by gas holdup, bubble diameter and power consumption. Therefore, a three-phase Eulerian equation with k-e turbulence model and additional models of two bubble diameter, a torque and a mass transfer coefficient were applied in the simulation. The simulation results were validated with experimental data and used to analyze the spatial distribution of the mass transfer coefficient. The results demonstrated that the simulation and experimental data of Sauter mean bubble diameter and power number were in good agreement and the simulation results of the mass transfer coefficient were agree with the values calculated by an empirical correlation. The Davoody model can be strongly recommended for further simulation of the bubble diameter, and the gas holdup and mass transfer coefficient were very unevenly distributed in the lower zone. Hence, the lower impeller clearance should be considered.

A computational fluid dynamics (CFD) simulation was performed to study the hydrodynamics characteristics in a Rushton turbine stirred tank in laminar regime. The effects of operating condition, working medium and geometrical parameter on the flow field and power number characteristics were investigated. It is found that the two-loop flow pattern is formed in laminar regime when the impeller is not very close to tank bottom, while its shape and size vary with Reynolds number and impeller diameter. For a given geometrical configuration, the flow pattern, power number and dimensionless velocity profile are mainly depended on Reynolds number, and do not change with working medium and scale-up for a constant Reynolds number. When impeller off-bottom clearance is too low and Reynolds number is relatively high, the fluid flow would transit from two-loop flow pattern to sing-loop flow pattern as that occurs in turbulent regime. Power number falls for larger impeller in laminar regime. Surprisingly, in laminar regime, power number in the baffled tank with small impeller is almost identical to that in the unbaffled tank.

Rotor-stator mixers are used in many industries to perform emulsification and de-agglomeration processes. Despite previous research, different modes of operation have not been compared in terms of flow and power characteristics. The aim of this study was to use CFD to investigate power and flow characteristics of a Silverson L5M mixer operating in batch and in-line mode. MRF was used along with the standard k - ∊ turbulence model for the simulations. Results suggest that batch mixers can be characterised in the same was as in-line mixers, and for a given mixing head design, the characterisation is independent of the mode of operation. A new way of the calculating flow number is proposed, which explains some discrepant results from previous studies. Overall, this work enhances our understanding of rotor-stator mixers and allows for better design choices of mixer.

The relationship between power and flow characteristics of batch rotor-stator mixers has been studied using CFD simulations with experimental power validation. The mixer studied was the Silverson L5M batch mixer with the standard emulsor head. The size of the holes in the screen and the constriction of the base hole were changed in small increments. The MRF technique was used to model rotor rotation. A model is developed in this study which links the power and flow numbers of the mixer. Since power is easy to measure experimentally, one can use this model to predict the flow number by measuring torque. A second model is also developed which allows one to predict the flow number using solely the geometry of the mixing head. This study greatly enhances our understanding of the relationship between power, flow and mixer geometry in rotor-stator mixers.

This paper is aimed to study the relationship between the kneading pressure, power consumption and the planetary motion parameters of a twin-blade planetary mixer for mixing highly viscous fluids by using CFD simulations. An experimental setup is built to measure the kneading pressure with a thin-film pressure sensor. A validated CFD model is used to investigated the kneading mechanism and hydrodynamic behaviors in the mixer. Results indicate that increasing the absolute speed and the speed ratio can significantly increase the maximum kneading pressure, while decreasing the absolute speed or increasing the speed ratio can effectively reduce the power consumption. The correlation of the kneading pressure with planetary motion parameters is obtained by proposing a specific pressure-oriented Reynolds number ReM-p and a pressure number Npmax and the correlation of the power consumption with planetary motion parameters is determined by introducing the improved Reynolds number Rei and power number Npi.

Mixing is an important operation in the chemical industry. The present numerical study, validated by experimental data, offers a computational framework for minimizing the stirred-tank reactor power consumption and the impeller equivalent stress. The flow pattern, turbulence parameters, and power consumption of the three types of impellers, named as 6-blade Rushton turbine and U-shape and V-shape impeller designs, are numerically studied using the Computational Fluid Dynamic (CFD) analysis. The interaction between the fluid and the solid is then studied through a two-way Fluid Structural/Solid Interaction (FSI) analysis. Multi-objective Genetic Algorithm (MOGA) is used along with both Direct Optimization (DO) and Response Surface Optimization (RSO) to optimize the blade’s geometrical parameters, including blade thickness (Tb), disk thickness (TD), and vertical angle of the blade (θ). The variation between experimental and numerical results, in terms of power consumption, is around 5%. The computational results show that the power number (Np) can decrease, respectively by 21% and 48%, for the V- and U-shape impellers compared to the 6-blade Rushton turbine. The maximum turbulent kinetic energy and the maximum dissipation rate of the turbulent kinetic energy of the U-shape (k = 0.065 m2/s2, e = 65.14 m2/s3) are more than V-shape impeller (k = 0.044 m2/s2, e = 25.16 m2/s3). The FSI results also show that the lowest von Mises stress occurs in the V-shape impeller.

The three-dimensional flow field generated by a coaxial mixer composed of double Scaba impellers and an anchor in the mixing of the xanthan gum solution, a non-Newtonian yield-pseudoplastic fluid was investigated using the computational fluid dynamics (CFD) technique. The mixing time measurements were performed by a non-intrusive flow visualization technique called electrical resistance tomography (ERT). To evaluate the influence of the impeller spacing on the hydrodynamics of the double Scaba-anchor coaxial mixer, the upper impeller submergence was set to 0.140 m while the lower impeller clearance and the spacing between two central impellers were changed within a wide range. The experiments and simulations were conducted for both co-rotating and counter-rotating regimes at different impeller spacing. The analysis of the collected data with respect to the power number, flow number, mixing time, and pumping effectiveness proved that the co-rotating mode had superiority over the counter-rotating regime. Fu...

Computational fluid dynamics (CFD) simulations were performed to predict the floating particles suspension in a baffled tank stirred by a standard Rushton turbine. An Eulerian multiphase model and a standard k-e turbulence model with mixture properties were used in the CFD simulation. The impeller rotation was solved using a moving reference frame method. Flow pattern, power number and solid holdup distribution were obtained and compared with the results in literature. The effects of operating condition on floating particles suspension characteristics were studied. It indicated that the influences of impeller speed and solid loading on particle suspension varied with particle sizes. For small particles, the impeller speed and solid loading have no obvious effects on solid holdup distribution and suspension quality. For large particles, particle suspension quality becomes better first, and then keeps almost unchanged with enhancing of the impeller speed. Suspension quality is better for higher solid loading of large particles. Within the scope of the present study, solid loading has no great effect on suspension quality. Suspension quality becomes worse with increasing of the particle size. Large particles are easy to accumulate in the centres of the liquid free surface and the upper circular loop, and the vicinity of the shaft.

In-line high shear mixers (HSMs) with ultrafine teeth are useful to intensify mixing and dispersive process with viscous fluids. However, the relationships among the flow pattern, the power consumption and design parameters are not understood deeply yet, which hindered the further equipment optimization and scale-up. In this article, the effects of two important structural parameters, tip-to-base clearance and shear gap width, on flow pattern and power consumption of HSM were explored by CFD simulation. The LES and laminar model in turbulent and laminar flow regime were used respectively in CFD simulation with Newtonian and non-Newtonian fluids. The results indicate that with the increase of tip-to-base clearance and shear gap width, the velocity and strain rate in mixing head reduce significantly while the area of dead zone increased. The power number constant K p and K s of the standard in-line HSM predicted by CFD simulation agree well with the experimental data with acceptable error. The correlations of the predicted K p and K s of all designs which show their linear relationship with the tip-to-base clearance in axial direction f /( f + h ) and power function with shear gap width in radial direction g/D. These results provide the guidance on process development and scale-up of in-line HSM with the ultrafine teeth for viscous fluids.

The performance of different configurations of coaxial mixers composed of a wall scraping anchor impeller in combination with two different or identical central high speed impellers in the agitation of the shear-thinning fluids with yield stress (e.g. xanthan gum solution) was investigated. These multi-impeller mixers are more compact for the larger scale of mixing operations. The coaxial mixers employed in this study were the Scaba-Scaba-anchor, Scaba-Rushton-anchor, Rushton-Scaba- anchor, Scaba-pitched blade-anchor, and pitched blade-Scaba-anchor. The quality of mixing achieved by these five coaxial mixers was assessed for the Reynolds numbers in the range of the laminar to the transitional regime in the co-rotating mode through computational fluid dynamic (CFD) and electrical resistance tomography (ERT) techniques. A new correlation was introduced for these complex configurations of the coaxial mixers by incorporating the Metzner-Otto constants ( K s ) of the different types of the central impellers into the Reynolds number. The experimental and CFD data were employed to evaluate the mixing intensification attained by these five coaxial mixers in regard to the power consumption, mixing time, velocity profiles, shear strain rate profiles, flow number, power number, and pumping effectiveness. The analysis of the collected data indicated that the intensification of mixing of the highly viscous non-Newtonian fluids achieved by the Scaba-pitched blade-anchor coaxial mixer was the highest among the mixing systems explored in this study.

Agitation is one of the greatest challenges in the computer simulation, which is a common operation in mixer–settlers. In the present work, hydrodynamic characteristics of delta impeller pump–mixers have been studied using computational fluid dynamics (CFD) simulations. Sliding mesh approach has been used for the modeling of interaction between static tank and rotating impeller. Standard k–e turbulence model was adopted. The effect of different geometrical parameters including off-bottom clearance, impeller diameter, number of blades and height of suction orifice on suction head and power consumption characteristics has been investigated. Low off-bottom clearance and high suction orifice location were found beneficial to suction increase without extra power input. Scale-up study has also been carried out at two different vessel sizes. CFD simulation results have been validated and agree with literature and experimental data. Optimum geometry of pump–mixer has been proposed, and new delta impeller designs have been proved better than the original one in pumping capacity. Scale-up study shows a close agreement of power number and head number of different geometric scales and confirms the validity of CFD simulation in scale-up of the delta impeller for industrial-scale application. Copyright © 2016 Curtin University of Technology and John Wiley & Sons, Ltd.

The main objectives of this work were to study the gassed power consumption and the local gas holdup for an aerated coaxial mixer composed of a wall scraping anchor and a central impeller. The working fluids were viscous corn syrup solutions at different concentrations. The central impellers were downward pumping pitched blade turbine, upward pumping pitched blade turbine, and hydrofoil A310 impellers. A novel correlation was developed to estimate the gassed power drawn by the coaxial mixer as a function of the gas flow rate, central impeller type, rotational speeds of the anchor and central impeller, and the ungassed power consumption by the anchor and the central impeller. To obtain a master power curve, two new correlations were proposed for the generalized power number and gas flow number of the aerated reactor furnished with the coaxial mixer by incorporating the equivalent rotational speed for the coaxial mixer, speed ratio (central impeller speed/anchor speed), and the central impeller power fraction into these two correlations. The experimental data revealed that by increasing the gas flow rate, the aerated anchor power was increased whereas the gassed power uptake of the central impeller was decreased. It was found that at the higher fluid viscosity and beyond the critical speed ratio equal to 10, the anchor power was increased by increasing the speed ratio (i.e. reducing the anchor speed). To measure the distribution of the gas holdup throughout the aerated reactor, four electrical resistance tomography planes were installed around the reactor. The tomography data showed that the local gas holdup near the vessel wall was not improved by increasing the anchor speed.

Performance analysis (ion transport per unit power consumption) of three different classes of flow promoters e.g. (i) twisted tape, (ii) twisted tape with cuts, and (iii) rod was tested in an electrodialysis setup with rectangular flow channel of fixed aspect ratio. Pressure drop inside flow channel with each flow promoter geometry was estimated at four different flow rates (5, 10, 15, 20 LPH). Comparison of Sherwood number, Sh, power number, Pn, Reynolds' number, Re and friction factor, f, indicated relative performance of any geometry with reference to the empty channel. 40% rise in Sh was recorded with monolayer layer twisted tape with spacing per unit membrane gap, d/h = 5.3 relative to empty channel. It is also reported that reduced spacing i.e. lower d/h did not show consistent improvement in ion transport. Twisted tapes causing uninterrupted swirling motion showed 80% better performance compared to twisted tape with cuts which caused an interrupted swirling flow at Re ~ 276.

The gassed power demand and volumetric mass transfer coefficient ( k L a ) were investigated in a fully baffled, dished-base stirred vessel with a diameter of 0.30 m agitated by five triple-impeller combinations. Six types of impellers (six-half-elliptical-blade disk turbine (HEDT), four-wide-blade hydrofoil impeller (WH) pumping down (D) and pumping up (U), parabolic-blade disk turbine (PDT), and CBY narrow blade (N) and wide blade (W)) were used to form five combinations identified by PDT + 2CBY N , PDT + 2CBY W , PDT + 2WH D , HEDT + 2WH D and HEDT + 2WH U , respectively. The results show that the relative power demand of HEDT + 2WH U is higher than that of other four impeller combinations under all operating conditions. At low superficial gas velocity ( u G ), k L a differences among impeller combinations are not obvious. However , when u G is high, PDT + 2WH D shows the best mass transfer performance and HEDT + 2WH U shows the worst mass transfer performance under all operating conditions. At high u G and a given power input, the impeller combinations with high agitation speed and big projection cross-sectional area lead to relatively high values of k L a . Based on the experimental data, the regressed correlations of gassed power number with Froude number and gas flow number, and k L a with power consumption and superficial gas velocity are obtained for five different impeller combinations, which could be used as guidance for industrial design.

Coaxial mixers are efficient in mixing of highly viscous fluids. The main objective of this study was to assess the power consumption for the gas dispersion in carboxymethyl cellulose solution, a power-law non-Newtonian fluid, with a coaxial mixer consisting of an anchor impeller and two central impellers as a function of the speed ratio (central impeller speed/anchor speed), fluid rheology, pumping direction of the central impeller, and the rotation mode (co-rotating vs. counter-rotating). This goal was achieved using both experimental and numerical approaches. A computational fluid dynamic model (CFD) was developed and validated using the experimental data. Electrical resistance tomography (ERT) was employed to measure the gas holdup. New equivalent impeller speed and diameter were defined and two novel correlations for the Power number and Reynolds number were proposed and successfully validated at different operating conditions. Additionally, new dimensionless correlations for the ratio of the gassed to un-gassed power consumption and the aerated power number as a function of the flow number, Froude number, and Reynolds number were developed and successfully tested for different coaxial mixing configurations.

The performances of the Standard κ-ε, RNG, Realizable, κ-ω and RSM turbulence models to describe the behavior of the flow in agitated tank reactors were evaluated. Because most of these tanks have complex geometries, structured meshing schemes are not a practical alternative in engineering. Two particular unstructured meshing schemes composed of either Cartesian Cut-Cell (CC) or Tetrahedral elements were tested in domains larger than 3 million cells. In this work, the blade thickness, which is usually disregarded, was accounted for. The performance of the turbulence models was validated by PIV measurements. A strong dependence on the grid size and the power number was found, with CC grids having good agreement with grids > 3.6 Million. The pumping number was independent of the cell number and the values agree with experimental data. The Realizable model resolved with a tetrahedral grid presented the overall best performance.

A quantitative methodology for particle suspension assessment is presented. A new parameter, fmov/tot, the ratio of the mean number of moving particles to the total number of particles, is introduced to evaluate the minimum speed required to just suspend solids. This approach is tested to investigate the impact of impeller clearance on the minimum impeller speed, Njs, in a vessel when using a radial flow Rushton turbine. Flow patterns and power numbers obtained experimentally and computationally support the suspension findings. Image analysis is an appropriate method for determining Njs. Lowering the impeller clearance reduces the speed required for particle suspension with a change of flow pattern from a radial discharge with two loops to a single loop scouring the vessel base. The power number also falls markedly at the two-to-one loop transition as does the strain rate near the base.

The power input in stirred bioreactors is an important scaling-up parameter and can be measured through the torque that acts on the impeller shaft during rotation. However, the experimental determination of the power input in small-scale vessels is still challenging due to relatively high friction losses inside typically used bushings, bearings and/or shaft seals and the accuracy of commercially available torque meters. Thus, only limited data for small-scale bioreactors, in particular single-use systems, is available in the literature, making comparisons among different single-use systems and their conventional counterparts difficult. This manuscript provides a protocol on how to measure power inputs in benchtop scale bioreactors over a wide range of turbulence conditions, which can be described by the dimensionless Reynolds number (Re). The aforementioned friction losses are effectively reduced by the use of an air bearing. The procedure on how to set up, conduct and evaluate a torque-based power input measurement, with special focus on cell culture typical agitation conditions with low to moderate turbulence (100 < Re < 2·104), is described in detail. The power input of several multi-use and single-use bioreactors is provided by the dimensionless power number (also called Newton number, P0), which is determined to be in the range of P0 ≈ 0.3 and P0 ≈ 4.5 for the maximum Reynolds numbers in the different bioreactors.

Homogeneous dispersion of particles is crucial for many processes where the reaction rate is highly dependent on relative rates of mixing or degree of homogenization. These processes include crystallization, polymerization, and some mineral-refining processes. Complete particle dispersion in high-concentration slurries is researched experimentally and numerically. Computation fluid dynamics results suggest that cloud height is an excellent indicator for mixing homogeneity, and energy efficiency can be enhanced by removing baffles over a range of solids concentrations under the complete dispersion condition. The power required to maintain a high cloud height in a stirred tank can be predicted via a simple power number analysis. The proposed unbaffled design can be potentially beneficial to some industrial processes like crystallization.